As is known in the art, a modulator-demodulator (modem) is an electronic device that modulates transmitted signals and demodulates received signals. The modem generally provides an interface between digital devices and an analog communications system to thus make possible analog transmission of digital information between two terminals or stations. Such transmissions may be over a transmission link such as a telephone line, cellular communication link, satellite link, and cable TV, each of which being generally band-limited. That is, the information may be transmitted across the transmission link only over a predetermined range of frequencies having a maximum bit error rate.
As is also known, a modem is used to provide wireless transmission between transmitting and receiving stations. Such wireless communication can be employed in a variety of applications: VHF, IS-54 (cellular), IS-95 (cellular), SPADE (satellite), GSM (cellular), HDTV, and SAT-TV, each using one of the following linear modulation techniques: QAM; QPSK; Pi/4 DPSK; GMSK. As with the transmission line application, the bandwidth of each is limited within an acceptable bit error rate.
While most modems are capable of providing compensation for Guassian noise, impulse noise is not well managed. Most modems also require higher powered amplification means since, in all cases, amplitude distortion is unacceptable. In broadcast environments, it is well understood that FM transmission provides superior impulse noise handling. Also in FM transmission schemes, the transmitted signal may be amplified with almost 100% efficiency since the information carrying portion of the signal is identified by the zero-crossings of the signal. Thus, amplitude distortion is ignored.
Despite these apparent advantages, only a few isolated examples exist of nonlinear frequency modulation used within modems. Frequency shift keying, providing a 300 bits per second data rate, essentially utilized two frequencies, each for representing a separate data bit. The next major development in modems was the use of phase modulation, beginning with two phase modulation, then four, then eight. A combination of amplitude and phase modulation was later developed, also referred to as quadrature amplitude modulation or QAM.
A subsequent development was Guassian minimum shift keying, or GMSK. At first glance, such coding resembles four phase modulation, though in order to avoid amplitude modulation, a special low pass filter referred to as a Guassian filter was applied to the data going into the phase modulator. Since some have regarded the Guassian filter as akin to an integrator, an argument could be made that such a modulation scheme results in frequency modulation, since GMSK can be demodulated with an FM discriminator. Yet, GMSK applies linear functions of the data to in-phase and quadrature carriers to produce a linear modulation; whereas, true FM is mathematically equivalent to the application of trigonometric functions of the filtered signal to an in-phase and quadrature carrier. FM is a non-linear modulation, which was perceived as inefficient for data transmission since the transmitted frequency spectrum is not a simple translation of the baseband spectrum as in AM modems. A further perceived problem with FM for a modem is that it only accepts real signals into its voltage controlled oscillator. That is, in the equivalent in-phase and quadrature carrier method for FM, both paths send the same data resulting in a double sideband spectrum of a single carrier, which was regarded as redundant and therefore inefficient compared to the double-sideband spectra of the dual in-phase and quadrature carriers of QAM modems. Also, single-sideband (SSB) transmission was considered undesirable for modems because there is no simple way to efficiently demodulate an AM-SSB signal without a carrier reference. FM was dismissed as an analog technique totally unrelated to data transfer except with regard to FSK.
In an ordinary modem, binary data is normally passed through a baseband raised-cosine filter which limits the bandwidth of the baseband signal so that when one multiplies the baseband signal by a carrier, control over the passband signal bandwidth is provided without intersymbol interference. The output of an ordinary modem includes signals having discrete phases such that data included therein can be identified by discerning the phase of each bit. For instance, whenever a signal has a +90° phase shift it is interpreted as 0 and when the phase shift is −90° it represents 1, etc. Thus, in an ordinary modem employing a carrier, the phase and/or amplitude of the carrier signal are determined by the current symbol being transmitted. The carrier assumes only selected values of phase and amplitude for most of the duration of each symbol and graphical plots of all the selected phase-amplitude pairs are called the constellation points of the modem. Ordinary modems require that there be distinct points in the constellation for each possible value of the transmitted symbol. Furthermore, bit errors occur in the receiver if the points are mis-assigned due to intersymbol interference or due to noise on the link.
In many applications the computational requirements of the modem introduce a delay which is detrimental to the operation of the system. For example, digital voice transmission and multiple access networks are sensitive to delay in the modem. Furthermore, the rate at which a modem may transmit and receive data per unit of bandwidth is called the modem bandwidth efficiency. In the discipline of Digital Information Theory this efficiency is known to be maximized when the transmitted signal has the maximum entropy or randomness. The maximum entropy transmission is band-limited Guassian noise, and among other properties Guassian noise will not dwell at a distinct phase-amplitude pair as in a constellation. Thus it is desirable to provide a modem having a passband carrier which minimizes the internal processing time and also maximizes the bandwidth efficiency without sacrificing bit error rate.
A method of communicating a sequential series of symbols over a transmission link comprises the steps of multi-rate polyphase filtering the symbols, using the filtered output to modulate a carrier, transmitting the modulated carrier across the transmission link, receiving the modulated signal, applying the inverse of the transmitter polyphase filter to the received signal, and thresholding and re-assembling the output of the inverse filter to recover the transmitted symbols.
Data is transmitted from a first modem to a second modem across a wireless transmission link by forming input data frames from the input data, multiplying the input frames by a rotation matrix, frequency modulating and transmitting the rotation matrix output, receiving and frequency demodulating the transmitted data, multiplying the demodulated signal by a second rotation matrix, and re-assembling the de-rotated data to recover the original data.
A modem for communicating symbols across a transmission link includes a transmit portion and a receive portion, wherein the transmit portion comprises a partitioning element for dividing the input into parallel data channels, a baseband transmit rotation section for polyphase transforming the channeled data into parallel signal channels, a re-arrangement of the parallel signal channels into sequential serial samples, a carrier modulator for providing a modulated signal, and a transmitter for transmitting the modulated signal. The receive portion comprises a receiver for receiving the transmitted, modulated signal, a demodulator for demodulating the received signal into parallel signal channels, a receive rotation section for polyphase transforming the demodulated, received signal into parallel data channels, and an assembling element for combining the parallel data channels into a serial data signal.
The polyphase filtration of these methods and this modem enables FM modulation of the transmitted symbols since only a real component of the original symbols is generated. FM, whether achieved using frequency modulation or phase modulation of the input signal, provides enhanced immunity to non-Guassian noise, provides high bandwidth efficiency, utilizes non-coherent IF and thus requires no carrier recovery, is of lower cost than conventional modems in part due to the absence of A/D converters, provides low co-interference due to the FM capture effect, and is compatible with analog signals, owing to the use of commuting operators. More power efficient, but potentially less linear amplifiers such as Class B and Class C can be employed since zero crossings are used to determine data content; carrier recovery is not required. Modems employing modulation schemes such as QAM cannot employ such non-linear amplification. Further, satellite modems employing the presently disclosed method and modem save on TWT backoff power and thus are more energy efficient since intermodulation is not a problem, while personal computers achieve higher data rates without sacrificing bit error rate.
Polyphase filtration is implemented in a first embodiment by a wavelet filter (e.g. Quadrature Mirror Filter) pair. The partitioning element partitions the serial data among plural, parallel data channels prior to linear-phase FIR vector filtration, the filter coefficients being square matrices, whereby the input data are transformed into parallel signal channels. The transformation is by way of a convolutional rotation of the input data vector. Each coordinate of the output signal is confined to a frequency sub-band which slightly overlaps its neighbor. Pre-emphasis in the transmit portion, prior to the rotation in a first embodiment, places most of the information in the lower baseband frequencies. This is due to the noise probability density function of an FM discriminator that is proportional to the square of the frequency. De-emphasis in the receiver results in an addition to the overall gain equation. This equation, in one embodiment, includes contributions by the FM transmitter gain, the de-emphasis gain, and a noise reduction gain. The pulse amplitude levels representing the partitioned data bits within each sub-band need not necessarily correspond to an integer number of bits, as long as all of the levels in all the subbands correspond to an integer value.
The receiver portion provides the de-rotation filter for performing a reverse transformation to recover the original data. In one embodiment, the reverse transformation commutes with the modulation transformation. In a further embodiment, the coefficients of the de-rotation filter in the receiver are adaptively selected for equalization to correct for transmission path distortion, since the analyzer is a fractional-rate FIR filter. Thus, a near-perfect reconstruction filter is employed. A threshold operator takes the nearest integer coordinate values as the most likely symbol.
In a further embodiment, the commuting rotation and de-rotation filters are derived from the elementary matrices which describe a geometric rotation of a vector. Their function is to transform an input data vector within a data coordinate system into a signal vector within a signal coordinate system such that the sequentially serialized coordinates of the signal vector would form the digital samples of a bandlimited analog signal. Yet another approach to the matrices is mathematical transformation by way of discrete wavelet transformations.
In each of the transmitter portion and receiver portion, the rotation operator is ideally a computationally efficient multi-rate wavelet filter bank. Logarithmic amplification of the baseband signal prior to introduction into the FM transmitter modulator results in an improvement in the modulation gain out of the receiver. Further, as a by-product of the logarithmic amplification prior to the transmitter and de-amplification after the receiver, noise introduced in the transmit channel is attenuated.
Dispersive impairments in the link may create a relative phase shift between sub-bands. In that case, the “orthogonality” of the wavelets is lost and cross terms appear as self-interference in the recovered symbols.